つつ details

write + while

kaki tsutsu

while; even as — formal/literary; marks either simultaneous action or, more often, a concession the subject is aware of

meaning: while writing

体からだに悪わるいと分かりわかりつつ、タバコをやめられない。

karada ni warui to wakari tsutsu, tabako o yamerarenai.

I can't quit smoking, while understanding it's bad for my health. neutral

彼女かのじょは微笑ほほえみつつ、静しずかにうなずいた。

kanojo wa hohoemitsutsu, shizuka ni unazuita.

She gave a quiet nod, smiling all the while. neutral

Examples

even though; while — a restrained, often self-directed concession over a fact the subject is aware of

体からだに悪わるいと分わかりつつ、タバコをやめられない。

karada ni warui to wakaritsutsu, tabako o yamerarenai.

I can't quit smoking, while understanding it's bad for my health. neutral

返事へんじをしなければと思おもいつつ、一週間いっしゅうかんが過すぎてしまった。

henji o shinakereba to omoitsutsu, isshuukan ga sugite shimatta.

Even while telling myself I had to reply, a whole week slipped by. neutral

当社とうしゃは、リスクを認識にんしきしつつ、この事業じぎょうへの投資とうしを決定けっていいたしました。

tousha wa, risuku o ninshiki shitsutsu, kono jigyou e no toushi o kettei itashimashita.

While recognizing the risk, our company has decided to invest in this venture. formal

while doing — two actions or states held at once by one subject, つつ's formal register partner of ながら

彼女かのじょは微笑ほほえみつつ、静しずかにうなずいた。

kanojo wa hohoemitsutsu, shizuka ni unazuita.

She gave a quiet nod, smiling all the while. neutral

ながら
つつ covers the same simultaneous-action ground as ながら but reads distinctly more formal and literary — comfortable in essays, reports, and news narration, stiff if dropped into casual chat, where ながら is the everyday default.
ながらも
Both push a concessive reading over plain simultaneity, but つつ needs no added も to carry "even though" on its own (知りつつ already reads as concession in writing), while ながら needs the も to tip out of neutral simultaneity into concession.

つつある
Same tail, unrelated grammar — つつ joins two actions or states within one clause (音楽を聞きつつ歩いた), while つつある fuses onto a single verb to mark a gradual change IN PROGRESS (増えつつある) and cannot take a second clause the way つつ does.